## Fluid Mechanics and Hydraulic Machinery Miscellaneous

#### Fluid Mechanics and Hydraulic Machinery

1. A phenomenon is modeled using-n dimensional variables with k primary dimensions. The number of non-dimensional variables is

1. NA

##### Correct Option: C

NA

1. The parameters which determines the friction factor for turbulent flow in a rough pipe are

1. NA

##### Correct Option: C

NA

1. A test is conducted on a one-fifth scale model of a Francis turbine under a head of 2 m and volumetric flow rate of 1 m3/s at 450 rpm. Take the water density and the acceleration due to gravity as 103 kg/m3 and 10 m/s2, respectively. Assume no losses both in model and prototype turbines. The power (in MW) of a full sized turbine while working under a head of 30 m is _______ (correct to two decimal places).

1.  Dm = 1 Dp 5

Model: H = 2 m, Q = 1 m3 /s
Prototype: H = 30 m, P =?
N = 450 rpm, ρ = 1000 kg/m3 /g = 10 m/s2
For model, pm = ρgQH = 1000 × 10 × 1 × 2 = 20 kW

= 29045.24 kW
= 29.05 mW

##### Correct Option: C

 Dm = 1 Dp 5

Model: H = 2 m, Q = 1 m3 /s
Prototype: H = 30 m, P =?
N = 450 rpm, ρ = 1000 kg/m3 /g = 10 m/s2
For model, pm = ρgQH = 1000 × 10 × 1 × 2 = 20 kW

= 29045.24 kW
= 29.05 mW

1. For a Pelton wheel with a given water jet velocity, the maximum output power from the Pelton wheel is obtained when the ratio of the bucket speed to the water jet speed is ______ (correct to two decimal places).

1. In pelton wheel:-

 η= 2(vu -u2) v2

where,
u = bucket speed
v = water jet speed
So, For maximum efficiency:-
 dx = 0 du

2(v – 2u) = 0 v = 2u
 u = v 2

##### Correct Option: A

In pelton wheel:-

 η= 2(vu -u2) v2

where,
u = bucket speed
v = water jet speed
So, For maximum efficiency:-
 dx = 0 du

2(v – 2u) = 0 v = 2u
 u = v 2

1. Which one of the following statements is TRUE?

1. Kaplan turbine is an axial-flow reaction turbine

##### Correct Option: D

Kaplan turbine is an axial-flow reaction turbine